Given the function:
[tex]h(x)=-3x^3-2x^2-8x-2[/tex]
Let's use the rational zeros theorem to list all possible rational zeros of the given polynomial.
To use the rational roots theorem we have:
[tex]\pm\frac{p}{q}[/tex]
Where p is a factor of the constaant (last term).
q is a factor of the leading coefficient,
Thus, we have:
p: Factors of -2 = ±1, ±2
q: Factors of -3 = ±1, ±3
The rational zero will be every combination of ±p/q.
Thus, we have:
[tex]\begin{gathered} \pm\frac{p}{q}=\pm\frac{1}{1},\pm\frac{1}{3},\pm\frac{2}{1},\pm\frac{2}{3} \\ \end{gathered}[/tex]
Simplify:
[tex]\pm\frac{p}{q}=\pm1,\pm\frac{1}{3},\pm2,\pm\frac{2}{3}[/tex]
Therefore, the list of all possible rational zeros are:
[tex]\pm1,\pm\frac{1}{3},\pm2,\pm\frac{2}{3}[/tex]
ANSWER:
[tex]\pm1,\pm\frac{1}{3},\pm2,\pm\frac{2}{3}[/tex]
